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Police later arrest a man they said tried to kidnap the 7-year-old girl

The suspect says, "I didn't bother nobody. I was never there"

A 7-year-old Georgia girl fought off a man who'd grabbed her in the aisle of a Walmart, with police eventually tracking down the suspect they accuse of attempted kidnapping.

Georgeann Baxter told HLN's Jane Velez-Mitchell that she was in the Bremen store with her daughter, Brittney, on Wednesday.

"We were walking around the Walmart, and we felt safe," the mother said, talking about how they were looking at Valentine's Day cards and toys in the west Georgia store, about 45 miles west of Atlanta.

When Baxter asked her daughter if she wanted to join her to get strawberries, the girl said that she wanted to stay in the toy aisle for a few more minutes.

Soon thereafter, surveillance video from the Walmart -- later released by Bremen police -- shows a man approaching her.

"He came up to me and started a conversation," Brittney recalled Thursday to HLN. "After ... I said, 'I'm going to get my Mommy."

The man is seen in the video picking up the young girl and starting to carry her away, as she flailed.

Brittney said she responded as she'd been taught by family, including her brother in the U.S. Army, and a school counselor in a lesson on how to respond if you're touched inappropriately.

"Punch, kick and scream as hard as you can, and then tell somebody that you trust," she said of what she did -- and what she'd tell others to do, if they're in the same situation.

Eventually, the man put the girl down and fled the store. Police later caught and arrested Thomas Woods, whom they accuse of trying to kidnap Brittney.

On Thursday, Woods, in his mid-20s, insisted to reporters -- including those from CNN affiliate WSB -- that he was innocent.

"I didn't bother nobody. I was never there," he said.

According to information from the Georgia Department of Corrections, Woods was released on parole last October after serving four and a half years of a 7-year term for voluntary manslaughter.

Bremen Police Chief Keith Pesnell told HLN that he favored changing the rules, so that there were greater restrictions on people who are convicted of violent crimes -- to prevent incidents like the one that allegedly happened to Brittney.

"I think it's time we have to look at things, for the safety of the children," Pesnell said. "Fortunately, things are in place to train our kids, and Brittney did exactly the right thing."

Speaking to HLN's Vinnie Politan, Emily Altman -- a counselor at the Tallapoosa Primary School -- said that she'd taught Brittney and other students as young as four years old some self-defense basics as part of a program called "Good Touch, Bad Touch."

"It's never too early to say, you stay right with mom, or you yell and scream if somebody were to (grab you)," Altman said of the program.

However she learned what to do, young Brittney responded "perfectly" to the alleged kidnapper, her counselor said.